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<head><title>statePolytope(Ideal) -- computes the state polytope of an ideal</title>
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<div><h1>statePolytope(Ideal) -- computes the state polytope of an ideal</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>statePolytope(I)</tt></div>
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<li><span>Function: <a href="_state__Polytope.html" title="computes state polytopes of ideals">statePolytope</a></span></li>
<li><div class="single">Inputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Ideal.html">ideal</a></span>, the ideal</span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___List.html">list</a></span>, the list of vertices of the state polytope</span></li>
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<div class="single"><h2>Description</h2>
<div>See Sturmfels's book <i>Groebner bases and convex polytopes</i>, page 14 for the definition of <i>State</i>(I). (The difference between this and <i>State</i><sub>m</sub>(I) is that for all sufficiently large m, <i>State</i><sub>m</sub>(I) does not distinguish between initial ideals which have the same saturation with regard to the irrelevant ideal, whereas in <i>State</i>(I), these are separated.) <table class="examples"><tr><td><pre>i1 : R = QQ[a..d];</pre>
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<tr><td><pre>i2 : I = ideal(a*c-b^2,a*d-b*c,b*d-c^2);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : statePolytope(I)
LP algorithm being used: "cddgmp".
polymake: used package cddlib
Implementation of the double description method of Motzkin et al.
Copyright by Komei Fukuda.
http://www.ifor.math.ethz.ch/~fukuda/cdd_home/cdd.html
VERTICES
1 11 7 7 11
1 11 3 15 7
1 8 6 18 4
1 6 9 18 3
1 3 15 15 3
1 7 15 3 11
1 4 18 6 8
1 3 18 9 6
o3 = {{11, 7, 7, 11}, {11, 3, 15, 7}, {8, 6, 18, 4}, {6, 9, 18, 3}, {3, 15,
------------------------------------------------------------------------
15, 3}, {7, 15, 3, 11}, {4, 18, 6, 8}, {3, 18, 9, 6}}
o3 : List</pre>
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